PIRSA:25110053 Conference Mathematical physics

DOI10.48660/25110053

Conference/School: Holomorphic-topological field theories and representation theory

Nawata, S. (2025). Branes and DAHA Representations. Perimeter Institute. https://pirsa.org/25110053

Nawata, Satoshi. Branes and DAHA Representations. Perimeter Institute, Nov. 04, 2025, https://pirsa.org/25110053 

@misc{ pirsa_PIRSA:25110053,
  doi = {10.48660/25110053},
  url = {https://pirsa.org/25110053},
  author = {Nawata, Satoshi},
  keywords = {Mathematical physics},
  language = {en},
  title = {Branes and DAHA Representations},
  publisher = {Perimeter Institute},
  year = {2025},
  month = {nov},
  note = {PIRSA:25110053 see, \url{https://pirsa.org}}
}

Abstract

In this talk, I will talk about the representation theory of the spherical double affine Hecke algebra (DAHA) of C∨ C1, using brane quantization. By showing a one-to-one correspondence between Lagrangian A-branes with compact support and finite-dimensional representations of the spherical DAHA, we provide evidence of derived equivalence between the A-brane category of SL(2,C)-character variety of a four-punctured sphere and the representation category of DAHA of C∨ C1. The D4 root system plays an essential role in understanding both the geometry and representation theory. In particular, this A-model approach reveals the action of an affine braid group of type D4 on the category.

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